On the degeneracy between w 0 and w a Yungui Gong Huazhong Univ of Science and Tech 华中科技大学 龚云贵 The 7 th Aegean Summer School, Paros, Greece,

Contents  Motivations: General Property of Scalar Field dynamics  Dark energy parametrizations  The degeneracy between w 0 and w a  The consequence of the derived degeneracy

Motivations  General Property of scalar field dynamics  scalar field as dark energy: Tracking solutions  Tracker fields (Steinhardt etal, PRD 1999)

Tracking Solutions

Tracking Solution: General Property  Almost independent of initial conditions  Relation  Common Dynamics for scalar fields

Efstathiou Parametrization  Dark energy parametrization: capture the main dynamics of scalar field MNRAS 383, 879 (1999)

CPL Parametrization  Approximation E. Linder astro-ph/

The degeneracy in CPL model  w 0 and w a is degenerated  What is the degeneracy? related with ?

Dark Energy Parametrizations (Partial Lists)  Dark energy parametrization: capture the main dynamics of scalar field  Efstathiou 1999, MNRAS 310, 842  CPL, Chevallier & Polarski 2001, IJMPD 10, 213; Linder 2003, PRL 90,  JBP, Jassal, Bagla & Padmanabhan, MNRAS 356, L11  Wetterich 2004, PLB 594, 17

Scalar Field approximation  Cosmological equations

Scalar Field Dynamics  Take the (Slow-roll) approximation  For Thawing scalar field Scherrer & Sen 2008, PRD 77,

approximation

Thawing scalar fields  Approximate w(z) dotted curve short dash curve long dash curve

The degeneracy between and  Relation  0 th order approximation Scherrer and Sen 2008, PRD 78,

SSLCPL model  Taylor Expansion Gong etal., Int. J. Mod. Phys. 22 (2013) ,

The accuracy of the approximation

SSWCPL model  Take approximation

The accuracy of the approximation

The degeneracy  Self-consistency

Flat SSLCPL Results

Flat SSWCPL Results

Flat CPL Results

Comparisons

Conclusions  The dynamics of scalar fields has some common features  The exists an approximate relation between w and  For thawing models, the dynamics can be approximated by CPL parametrization with degenerated relation between w 0 and w a  The reduced degeneracy helps improve the constraint on w(z)

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